Daniel Alan Goldston (born January 4, 1954, in

Oakland, California Oakland is a city in the East Bay region of the San Francisco Bay Area in the U.S. state of California. It is the county seat and most populous city in Alameda County, California, Alameda County, with a population of 440,646 in 2020. A major We ...

) is an American mathematician who specializes in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. He is currently a professor of mathematics at

San Jose State University San José State University (San Jose State or SJSU) is a Public university, public research university in San Jose, California. Established in 1857, SJSU is the List of oldest schools in California, oldest public university on the West Coast of ...

Early life and education

Daniel Alan Goldston was born on January 4, 1954, in Oakland, California. In 1972, he matriculated to the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, where he earned his bachelor's degree and, in 1981, a Ph.D. in mathematics. His doctoral advisor at Berkeley was Russell Sherman Lehman; his dissertation was entitled "Large Differences between Consecutive Prime Numbers".

Career

After earning his doctorate, Goldston worked at the University of Minnesota Duluth and then spent the next academic year (1982–83) at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

(IAS) in Princeton. He has worked at

since 1983, save for stints at the IAS (1990), the

University of Toronto The University of Toronto (UToronto or U of T) is a public university, public research university whose main campus is located on the grounds that surround Queen's Park (Toronto), Queen's Park in Toronto, Ontario, Canada. It was founded by ...

(1994), and the Mathematical Sciences Research Institute in Berkeley (1999).

Research

In 2009, Goldston, János Pintz, and Cem Yıldırım proved:

\liminf_\frac=0

where

p_n

denotes the n^th

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

. In other words, for every

c>0\

, there exist infinitely many pairs of consecutive primes

p_n\

and

p_\

which are closer to each other than the average distance between consecutive primes by a factor of

c\

, i.e.,

p_-p_n . This result was originally reported in 2003 by Goldston and Yıldırım but was later retracted. Then Pintz joined the team and they completed the proof with the GPY sieve .

Recognition

In 2014, Goldston won the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to numbe ...

, shared with Yitang Zhang and colleagues Cem Yildirim and János Pintz, for his contributions to

. Also, Goldston was named to the 2021 class of fellows of the American Mathematical Society "for contributions to

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

References

External links